Nonmesonic Weak Decay of $\Lambda$ Hypernuclei: The Three--Nucleon Induced Mode

0.17 MB·

by  E. Bauer

Λ
Nonmesonic Weak Decay of Hypernuclei:
The Three–Nucleon Induced Mode
E. Bauer1,2, G. Garbarino3 and C. A. Rodr´ıguez Pen˜a2
7 1Facultad de Ciencias Astrono´micas y Geof´ısicas,
1
0 UNLP, 1900-La Plata, Argentina
2
2 IFLP, CONICET, 1900-La Plata, Argentina

n
a 3IIS G. Peano, I-10147 Torino, Italy
J

4
1
Abstract

]
h
-t The nonmesonic weak decay of Λ hypernuclei is studied within a microscopic dia-
l
c grammatic approach which is extended to include the three–nucleon induced mech-
u
anism. We adopt a nuclear matter formalism which, through the local density ap-
n
proximation, allows us to model finite hypernuclei, a one–meson–exchange weak
[

transition potential and a Bonn nucleon–nucleon strong potential. One–, two– and
1
v three–nucleon induced weak decay rates are predicted for 1Λ2C by including ground
7 state correlations up to second order in the nucleon–nucleon potential and the re-
5
coil of the residual nucleus. Three–nucleon stimulated decays, ΛNNN → nNNN
9
3 (N = n or p), are considered here for the first time. The obtained decay rates com-
0 pare well with the latest KEK and FINUDA data. The three–nucleon induced rate
.
1 turns out to be dominated by nnp– and npp–induced decays, it amounts to ∼ 7%
0
of the total nonmesonic rate and it is ∼ 1/2 of the neutron–induced decay rate. The
7
reduction effect of the nuclear recoil is particularly relevant for the three–nucleon
1
: induced rates (∼ 15%), less important for the two–nucleon induced rates (∼ 4%)
v
i and negligible for the one–nucleon induced rates. Given the non–negligible size of
X
the three–nucleon induced contribution and consequently its importance in the pre-
r
a cise determination of the complete set of decay rates, new measurements and/or
experimental analysis are encouraged.
Key words: Λ Hypernuclei, Nonmesonic Weak Decay
PACS: 21.80.+a, 25.80.Pw, 13.30.Eg
Preprint submitted to Physics Letters B 17 January 2017
Introduction – Since the first observation of Λ hypernuclei in 1953 and the
introduction of the strangeness quantum number in the same year, strange
nuclei have been investigated with increasing theoretical and experimental
efforts[1].Hypernuclearphysicsisnowadaysamaturefieldofresearchwhichin
manyaspectsislocatedatthecrossroadsbetweenparticleandnuclear physics.
It implies important connections with QCD [2] —consider the relevance of
the production of hypernuclei and anti–hypernuclei in relativistic heavy–ion
collisions and the possible extension of the usual techniques of lattice QCD,
effective field theories and chiral perturbation theory to the baryon–baryon
interactions in the strange sector— as well as with astrophysical processes
and observables [3], where it provides important inputs to study the thermal
evolution, the stability, the macroscopic properties and the composition of
compact astrophysical objects, including the so–called “hyperon puzzle” in
neutron stars.
Production, structure and decays are the available tools to investigate those
properties of hypernuclei which in turn allow us to have access to the elemen-
tary weak and strong hyperon interactions within the flavor SU(3) sector [1];
the amount of information needed to this end would be practically impossible
to obtain in scattering experiments.
A Λ–hypernucleus weakly decays to non–strange final states by mesonic (Λ →
π−p and Λ → π0n) and nonmesonic modes (one–nucleon induced, ΛN → nN,
two–nucleon induced, ΛNN → nNN, etc, N denoting either a neutron or
a proton). A satisfactory theory–experiment agreement has been reached for
the mesonic weak decay and allowed us to test the proposed pion–nucleus
optical potentials. Most of the efforts have been devoted to the study of the
nonmesonic weak decay, which from the beginning in the seventies posed im-
portant and subtle questions.
Most of the long–standing problems concerning the nonmesonic weak decay,
which consisted in severe disagreements between theoretical and experimental
predictions, have been solved in the last ten years or so [1,4]: we mention the
“Γ /Γ puzzle” on the ratio between the decay rates for the neutron– and the
n p
proton–induced processes, Λn → nn and Λp → np, and the “asymmetry puz-
zle” in the decay of polarized hypernuclei. Different measurements of single
and coincidence spectra of the nucleons emitted in hypernuclear nonmesonic
decay, by theSKS Collaborationat KEK [5,6] andthe FINUDACollaboration
at LNF [7–9], their theoretical analysis and the many calculations incorporat-
ing: 1) complete meson–exchange weak interaction potentials (with both one–
and two–meson exchange) [10–13], 2) the description of the ΛN and NN
short–range correlations in terms of quark degrees of freedom [14], 3) two–
nucleon induced modes, ΛNN → nNN [15–20], as well as 4) nucleon final
state interactions [21–23], have proven crucial to solve the “Γ /Γ puzzle”,
n p
in a continuous dialogue and exchange between theory and experiment. The
2
two–nucleon induced decay mechanism is rather well understood at present
too, although the data on Γ are still affected by large error bars. Concerning
2
the asymmetry parameter in the nonmesonic decay of polarized hypernuclei,
webrieflyrecallthattheoretical modelsincluding theexchangeofuncorrelated
and correlated pion pairs (in addition to one–meson exchanges) and nucleon
final state interactions [24] solved the “asymmetry puzzle” by reproducing the
small asymmetry values measured at KEK [25].
As mentioned, the present agreement between theory and experiment on the
nonmesonic decay rates and asymmetries of s– and p–shell hypernuclei is
rather good, although the relatively large experimental error bars do not allow
us to discriminate between the various proposed weak interaction schemes.
One should remember that involved nuclear many–body processes such as
multinucleon induced nonmesonic weak decays and nucleon final state inter-
actions due to the nucleon–nucleon strong interaction complicate the extrac-
tion of the relevant elementary information. Discrepancies between theory and
experiment indeed remain and mainly concern proton emission, i.e., proton ki-
netic energy spectra and neutron–proton angular and momentum correlation
spectra [4,23]. A detailed description of the hyperon weak interactions under-
lying hypernuclear decay is thus impossible at present. From the theoretical
viewpoint, new decay mechanisms should be explored.
An aspect to be investigated concerns the possible relevance of multinucleon
induced decay mechanisms beyond the two–nucleon induced one. The aim of
the present work is to present the first evaluation of the rates for the three–
nucleon induced nonmesonic weak decays, ΛNNN → nNNN, which pro-
ceed through the following isospin channels: Λnnn → nnnn, Λnnp → nnnp,
Λnpp → nnpp, and Λppp → nppp. The effect of the nuclear recoil is also
taken into account as a new feature of our approach, which is applied to 12C.
Λ
Formally, this corresponds to implement translational invariance and exact
momentum conservation in the nonmesonic decays. The same microscopic ap-
proach showed that ground state correlation contributions are crucial for a
detailed calculation of the rates, the asymmetry parameter and the nucleon
emission spectra [19,20,22,24]. Less pronounced effects were reported by in-
cluding the ∆–baryon resonance [23].
Formalism – Let us start the discussion of our formalism by establishing the
notation adopted for the decay rates. The total nonmesonic decay rate reads:
Γ = Γ +Γ +Γ , (1)
NM 1 2 3
where Γ , Γ and Γ denote the rates for the one–, two– and three–nucleon
1 2 3
stimulated decays, ΛN → nN, ΛNN → nNN and ΛNNN → nNNN, where
N = n or p. In terms of the various isospin channels, the one–, two– and
three–nucleon induced nonmesonic rates are decomposed as:
3
Γ =Γ +Γ , (2)
1 n p
Γ =Γ +Γ +Γ , (3)
2 nn np pp
Γ =Γ +Γ +Γ +Γ . (4)
3 nnn nnp npp ppp
Thesub–indices ontherhsexpressions indicatetheinitial(multi)nucleon state
stimulating the weak decay: Γ ≡ Γ(Λnnp → nnnp), etc.
nnp
The analytical expressions for the nonmesonic decay widths are derived as
follows. To obtain the one–, two– and three–nucleon induced rates for a Λ
with four–momentum k = (k ,k) inside infinite nuclear matter with Fermi
0
momentum k , we start by the partial widths:
F
Γ (k,k ) = |hf|VΛN→nN|0i |2δ(E −E ) , (5)
1(2,3) F kF f 0
f
X
where |0i and |fi are the initial hypernuclear ground state (whose energy is
kF
E ) and the possible 2p1h, 3p2h or 4p3h final states (with energy E ), respec-
0 f
tively. The 2p1h (3p2h, 4p3h) final states define the rate Γ (Γ , Γ ), while
1 2 3
VΛN→nN is the two–body weak transition potential. This potential contains
the exchange of the full set of mesons of the pseudoscalar (π, η, K) and vec-
∗
tor octets (ρ, ω, K ), with strong coupling constants and cut–off parameters
deduced from the Nijmegen soft–core interaction NSC97f [26] (for details on
the weak transition potential we refer to [10]).
The rates for a finite hypernucleus are obtained by the local density approxi-
mation [27], i.e., after averaging the above partial widths over the Λ momen-
tum distribution in the considered hypernucleus, |ψ (k)|2, and over the local
Λ
Fermi momentum, k (r) = {3π2ρ(r)/2}1/3, ρ(r) being the density profile of
F
e
the hypernuclear core. One thus has:
Γ = dk|ψ (k)|2 dr|ψ (r)|2Γ (k,k (r)) , (6)
1(2,3) Λ Λ 1(2,3) F
Z Z
e
where for ψ (r), the Fourier transform of ψ (k), we adopt the 1s harmonic
Λ Λ 1/2
oscillator wave–function with frequency ~ω (= 10.8 MeV for 12C) adjusted
Λ
e
to the experimental energy separation between the s and p Λ–levels in the
hypernucleus. The Λ total energy in Eqs. (5) and (6) is given by k = m +
0 Λ
k2/(2m )+V , V (= −10.8 MeV for 12C) being a binding energy term.
Λ Λ Λ Λ
One should keep in mind that, by definition, the decay widths cannot contain
any (final state) interaction amongtheweak decay nucleons [20].Nevertheless,
in our approach the strong nucleon–nucleon interaction, VNN, plays a role in
the definition of the hypernuclear ground state, which, using perturbation
theory up to second order in VNN, reads:
4
h2p2h|VNN| i
|0i =N(k ) | i− |2p2hi (7)
kF F 2p2h E2p2h −EHF
X
h3p3h|VNN|2p2hi h2p2h|VNN| i
+ |3p3hi ⊗|Λi ,
3p3h2p2h (E3p3h −EHF)(E2p2h −EHF) !
X X
where | i (|Λi) is the normalized and uncorrelated hypernuclear core ground
state (hyperon initial state), i.e., the Hartree–Fock vacuum with energy E ,
HF
which we take equal to zero. For the nucleon–nucleon interaction VNN we
adopt a Bonn potential (with the exchange of π, ρ, σ and ω mesons) [28].
Note that being VNN a two–body operator, it can connect | i only to a
2p2h configuration, as shown in the second and third terms in the rhs of
the above expression. As our aim is to evaluate the decay rates up to Γ , we
3
have restricted the third term in Eq. (7) to 3p3h final states. It is self–evident
that E and E are the energies of the 2p2h and 3p3h configurations,
2p2h 3p3h
respectively. Moreover, N(k ) is the normalization function, which is easily
F
evaluated by imposing h0|0i = 1.
kF kF
The widths Γ , Γ and Γ are obtained by inserting Eq. (7) into Eq. (5)
1 2 3
and then by performing the local density approximation through Eq. (6). In
what follows, we focus on Γ (for a detailed discussion on Γ and Γ we refer
3 1 2
to [19,20]), for which one obtains:
Γ (k,k )=N 2(k ) δ(E −E ) hf|VΛN→nN|3p3h;Λi
3 F F f 0 (cid:12)
f=4p3h (cid:12)2p2h 3p3h
X (cid:12)X X
h3p3h|VNN|2p2hi h2p2h(cid:12)(cid:12)|VNN| i 2
× (cid:12) .
(E3p3h −EHF)(E2p2h −EHF) (cid:12)
(cid:12)
(cid:12)
(cid:12)
(cid:12)
The Goldstone diagrams contributing to the three–nucleon induced decay
mode are given in Fig. 1. Explicit expressions for these diagrams are obtained,
as usual, using the standard rules for Goldstone diagrams. We remind the
reader that our microscopic approach is inspired by the many–body scheme
proposed by Oset and Salcedo in [27] for the calculation of the one–nucleon
stimulated decay ratesandthen extended totwo–nucleon stimulated processes
in [16,17]. Although we adopt here a more realistic weak transition potential,
the parts concerning the exchange of the π and ρ mesons are the same of
[16,17,27].
Results – In Table 1 we give, for 12C, the contributions of the Goldstone
Λ
diagrams ofFig. 1 to the various isospin channels of the three–nucleon induced
decay mode. The effect of nuclear recoil is not included in these predictions.
The nnp– and npp–induced contributions dominate and are of the same order
of magnitude for most of the diagrams. The interference terms, AB, AC and
5
AA BB CC
(cid:1) (cid:2) (cid:3)
AB AC BC
(cid:1) (cid:2) (cid:3)
Fig. 1. Goldstone diagrams contributing to the three–nucleon induced decay rate.
The cuts indicating the 4p3h final states are also reported.
BC,someofwhich arenegative, providesmall contributions. Neglecting them,
the total three–nucleon induced rate would be ∼ 5% smaller than the full
result, Γ = 8.209×10−2 in units of the free Λ decay rate. For the complete
3
calculation we obtain (see last line in Table 1), Γ : Γ : Γ : Γ =
nnn nnp npp ppp
1 : 31 : 40 : 2.4. The dominance of the nnp– and ppn–induced decay modes
originates from the relative importance of the different isospin channels in a
twofold way: it is due to the isospin factors and the way in which the weak
and the strong interactions weight these factors in Eqs. (5) and (7). It turns
out that the exchange of vector mesons provide dominant nnp– and npp–
induced contributions by the charge–exchange terms. The scalar mesons have
smaller isospin factors and, together with the weights given by the different
interactions, softens the dominance behavior by the vector mesons. In Table
Table 1
Predictions for the isospin contributions to the three–nucleon induced decay mode
of 12C originating from the diagrams of Fig.1 (in units of 10−2 times the free Λ
Λ
decay rate).
Diagram Γ Γ Γ Γ Γ
nnn nnp npp ppp 3
AA 0.038 1.367 1.281 0.097 2.783
BB 0.037 1.064 1.448 0.091 2.640
CC 0.032 0.825 1.422 0.081 2.360
AB 0.008 0.116 0.135 0.005 0.264
AC −0.002 0.011 0.070 −0.004 0.075
BC −0.003 0.051 0.047 −0.008 0.087
sum 0.110 3.434 4.403 0.262 8.209
6
2 the full result for Γ is compared with the partial predictions obtained by
3
limitingtheweaktransitionpotentialto1)one–pion–exchangeand2)(π+K)–
exchange. As expected, the π–meson provides the largest contribution to the
decay width, while the effect of the K–meson is to reduce the rate.
Table 2
Effect of the weak transition potential on the total three–nucleon stimulated decay
width. The predictions for π– and (π + K)–exchange are compared with the full
result including the exchange of all mesons. Units are the same as in Table 1.
Weak Potential Γ
3
π 6.841
π+K 5.755
∗
π+η+K +ρ+ω+K 8.209
It is evident from Fig. 1 that we have restricted ourselves to the evaluation
of direct diagrams in which the weak and strong interactions are attached
to particles lines. We have neglected diagrams in which at least one of these
interactions is connected to a hole line as well as Pauli exchange diagrams.
The contributions of the “hole diagrams” are known to be small due to phase
space considerations; their net effect would be an increase in the value for the
three–nucleon induced decay width. On the contrary, exchange terms would
reduce the value of Γ . A rough estimate of the neglected diagrams can be
3
made by using our prior knowledge on the two–nucleon induced mechanism.
In [19] we evaluated the full set of diagrams for Γ by using the same micro-
2
scopic approach and weak and strong potentials of the present calculation.
The reduction due to the exchange terms turns out to be stronger than the
increase due to the neglected hole diagrams, resulting in a net decrease of Γ
2
by ∼ 20%. We expect a reduction of the same order of magnitude for Γ once
3
hole and exchange diagrams are taken into account. The evaluation of these
effects is quite involved and goes beyond the scope of the present contribution.
Nuclear recoil is particularly easy to implement within our nuclear matter
formalism, as we work in the momentum space. In particular, thesum over the
final states in Eq. (5) contains a summation over the momenta of the outgoing
nucleons ~p , where j = 1,...,i + 1 for the rate Γ (i = 1,2,3). Momentum
j i
conservation is expressed as: p~ +...+~p = −P~ , P~ being the momentum
1 i+1 T T
of the residual nucleus. The final nucleons are free particles; if we also assume
that the residual nucleus is in its ground state, all the final state particles
are characterized by their kinetic energy. The effect of nuclear recoil on the
decay rates thus results from subtracting the kinetic energy of the residual
nucleus from the Λ total energy k , thus replacing k with k − P2/2M ,
0 0 0 T res
M being the mass of the recoiling nucleus. In Table 3 we show the effect
res
of the recoil on the decay widths Γ , Γ and Γ . It tends to decrease, on
1 2 3
7
average, themomentaofthefinalnucleons, whicharethenmorePauli blocked.
We indeed found a reduction effect due to the recoil, which is particularly
relevant for Γ (∼ 15%), less important for Γ (∼ 4%) and negligible for Γ ;
3 2 1
for the total nonmesonic rate Γ the decrease is ∼ 3%. As expected, the
NM
reduction of the final nucleon momenta, i.e., of the decay rate, increases with
the number of nucleons produced in the decay. Note also that the rate Γ
1
is strongly dominated by the back–to–back kinematic for the final nucleon
pair, i.e., by small values of |P |. At variance, nucleons are emitted with
T
almost no preferential relative directions in two– and three–nucleon induced
decays, resulting in values of |P | which can be significant and producing
T
non–vanishing reductions of Γ and (especially) Γ . Another comment is in
2 3
Table 3
Effect of the recoil of the residual nucleus on the one–, two– and three–nucleon
stimulated decay widths of 12C. Results are given in units of the free Λ decay rate.
Λ
Γ Γ Γ Γ
1 2 3 NM
without 0.601 0.301 0.082 0.984
with 0.600 0.288 0.070 0.958
order on the final results for Γ , Γ and Γ of Table 3. The average momentum
1 2 3
for the nucleons emitted in three–nucleon induced decays is ∼ 290 MeV/c,
a value which is only slightly larger than the Fermi momentum of nuclear
matter, k ∼ 270 MeV/c. The Pauli blocking on these nucleons is thus severe
F
and contributes to the small value of the ratio Γ /Γ , which turns out to be ∼
3 1
0.12. Moreover, our predictions implies that Γ /Γ (∼ 0.48) > Γ /Γ (∼ 0.24),
2 1 3 2
which indicates that decays induced by four or more nucleons are expected to
be negligible.
In Table 4 we present the comparison of our final results for the full set of 12C
Λ
decay widths with the latest KEK [6] and FINUDA [8,9] data. A few details
on the experiments are needed for a better understanding of the comparison.
The first (second) FINUDAdetermination of Γ /Γ andthe data for Γ refer
2 NM p
to proton (neutron–proton correlation) spectra analyses. The determinations
listed as KEK–FINUDA have been reconstructed in the FINUDA paper [9]
by starting from various existing KEK data on Γ and the total (Γ ) and
p T
mesonic rates (Γ ), together with FINUDA values for Γ and Γ . The KEK–
M p 2
FINUDA rate Γ (Γ and Γ ) is obtained as the difference Γ = Γ −
n 1 NM n T
Γ − Γ − Γ (Γ = Γ − Γ − Γ and Γ = Γ − Γ ). Moreover, the
M p 2 1 T M 2 NM T M
KEK–FINUDA result for Γ is nothing but the weighted average between
p
the KEK and FINUDA determinations. The KEK determination Γ /Γ =
n p
0.51±0.14wasconsideredtobefreefromambiguitiesduetonucleonfinalstate
interactions and two–nucleon induced decays in [6]. Actually, these processes
are responsible for a non–negligible reduction of the experimental value of
Γ /Γ [1,4]: the determination Γ /Γ = 0.29 ± 0.14 (0.34 ± 0.15) shown in
n p n p
Table 4 is a theoretical fit of KEK coincidence nn and np spectra obtained
8
Table 4
Predictions and recent data from KEK–E508 [6] and FINUDA [8,9] for the non-
mesonic weak decay widths of 12C (in units of the free Λ decay rate). See text for
Λ
details.
Our KEK–E508 [6] FINUDA [8] KEK–FINUDA [9]
Γ 0.145 0.23±0.08 0.28±0.12
n
Γ 0.455 0.45±0.10 0.65±0.19 0.493±0.088
p
Γ 0.600 0.68±0.13 0.78±0.09
1
Γ 0.288 0.27±0.13 0.178±0.076
2
Γ 0.070 − − −
3
Γ 0.958 0.953±0.044 0.96±0.04
NM
Γ /Γ 0.319 0.51±0.14 0.58±0.27
n p
0.29±0.14 [21]
0.34±0.15 [22]
Γ /Γ 0.626 0.71±0.14 0.81±0.10
1 NM
Γ /Γ 0.301 0.29±0.13 0.25±0.12±0.02 0.19±0.08
2 NM
0.20±0.08+0.04
−0.03
Γ /Γ 0.073 − − −
3 NM
within the present microscopic approach in [21] (a finite nucleus calculation
in [22]) by including the mentioned many–body effects. These effects lead to
the inequality Γ /Γ < N /N = 0.51±0.14.
n p nn np
An overall agreement of our predictions with the experiments is evident from
Table 4, especially with KEK data (it is of the same quality as the compar-
ison between the central values of KEK and FINUDA data). Note how the
agreement is especially good for the most easily measurable rate, Γ , while
NM
for Γ , the rate affected by the largest error bars together with Γ , the agree-
n 2
ment is worse. The prediction for the Γ /Γ ratio compares well with the fits
n p
of [21,22] to KEK spectra. The only discrepancies which exceeds the level of
1σ are with the KEK–FINUDA rates Γ (and then Γ ) and Γ and the KEK
n 1 2
Γ /Γ ratio obtained without including the two–nucleon induced mode and
n p
final state interaction (see the discussion of the previous paragraph on the
experimental determinations of Γ and Γ /Γ ).
n n p
The rate Γ amounts to ∼ 7% of the total nonmesonic rate Γ and is about
3 NM
a half of the neutron–induced rate Γ . Therefore, the three–nucleon induced
n
contribution cannot be neglected if one aims at a detailed understanding of
the full set of decay rates. We finally note that the KEK and KEK–FINUDA
determinations of Γ tend to overestimate the value predicted here; given the
1
9
good agreement for Γ , one cannot exclude the eventuality that the KEK
NM
and FINUDA experiments counted a fraction of nucleons originating from
three–nucleon induced decays (and from two–nucleon induced decays too, in
the case of FINUDA) as wrongly produced by one–nucleon induced processes.
Conclusion – The first study of the three–nucleon stimulated nonmesonic
weak decay of hypernuclei is presented within a microscopic approach. The
full set of decay rates are obtained for 12C also including the effect of nuclear
Λ
recoil. The three–nucleon induced rate Γ turns out to be non–negligible —
3
amounting to ∼ 7% of Γ and being Γ /Γ ∼ 1/2— and is dominated by the
NM 3 n
nnp– and npp–induced channels. Nuclear recoil basically only affects Γ . The
3
predictions show a good overall agreement with present KEK and FINUDA
data.
In spite of the last advances in the field of nonmesonic decay, discrepancies
between theory and experiment persist and mainly concern emission spectra
involving protons. The results obtained in the present Letter for the three–
nucleon stimulated decays can hardly improve this disagreement, as these
decays are expected to provide almost the same proportion of weak decay,
i.e., primary, neutrons and protons (Γ ∼ Γ ∼ Γ /2). However, note
nnp npp 3
that additional, secondary nucleons coming from final state interactions (not
included here in the calculation of the decay rates) must be taken into account
in spectra analysis. It is also worth mentioning that the quality of present data
does not allow us to establish the degree of violation of the ∆I = 1/2 isospin
rule in the one–nucleon induced nonmesonic weak decay [4,29]. Most of the
adopted meson–exchange models, including the present one, only contain pure
∆I = 1/2 transitions. Further work is thus necessary to achieve the primary
purpose of hypernuclear weak decay studies, which is to access the properties
of the elementary strangeness–changing hyperon interactions. The efforts of
the recent years clearly indicates that nuclear many–body effects cannot be
disregarded nor easily disentangled from the basic weak decay ingredients;
mechanisms such as nucleon final state interactions and multinucleon induced
decays are relevant, they partially superimpose with one another and mask
the elementary weak interactions.
Outlook – Systematic and more precise measurements of nucleon spectra,
decay widths and asymmetries —possibly over some mass number range, as
in the spirit of FINUDA and under a close collaboration with theoreticians—
will be essential to move forward. An approved proposal at J–PARC consists
in the E18 experiment [30]. It is designed to have much better statistics than
KEK–E508 and concerns measurements of the rates Γ , Γ and Γ for 11B and
n p 2 Λ
12C. Triple nucleon coincidence measurements could lead to (the first) direct
Λ
measurements of Γ with a 10% statistical error. The kinematics of precise
2
triple coincidence measurements could provide some evidence of the three–
nucleon induced decay mode. Perhaps, an experiment with slightly improved
10